We report the layer-number dependence of the averaged interlayer thermal
resistances (R-int) of the suspended and supported few-layer graphene
(FLG), simulated by equilibrium molecular dynamics (EMD). The existence
of a silicon dioxide substrate significantly decreases the R-int of FLG
at low layer number. We use the model of long-wavelength dynamics of a
nanolayer adsorbed on a deformable crystal Kosevich and Syrkin, Phys.
Lett. A 135, 298 (1989) to explain the appearance of the substrate-
induced gaps in the FLG dispersion curves and phonon radiation into the
deformable substrate from these gap modes. The enhanced thermal
conductance in the cross-plane direction is ascribed to the phonon
radiation from FLG into the deformable substrate, which partially
transfers the flow of phonon energy in FLG from the in-plane to the
cross-plane direction and to the substrate. To confirm this, we
calculate the cross-plane thermal resistance of three-layer graphene
supported by an effective SiO2 substrate in which atomic masses are
increased by a factor of 1000. This makes the substrate almost immovable
and suppresses phonon radiation from the supported FLG by complete
phonon reflection at the interface. The cross-plane thermal resistance
of three-layer graphene supported on such a substrate is found to be the
same as its suspended counterpart.